volume | PIER Journals

Abstract

Various electromagnetic scattering approximations beyond the Born assumption have been published during the recent years. This paper introduces a simple framework of analyses and investigates in a systematic way the fundamentals of the proposed theories. Our main focus is to demonstrate the link and similarities between the different scattering approximations employing a common physical basis. Based on analogies established we try to bridge the apparent gap between existing theories as well as introducing possible extensions and refinements.

1. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor sphere," J. of Electromagn. Waves and Appl., Vol. 20, No. 12, 1569-1576, 2006.
doi:10.1163/156939306779292390 Google Scholar

2. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor cylinder," J. of Electromagn. Waves and Appl., Vol. 20, No. 13, 1853-1860, 2006.
doi:10.1163/156939306779292219 Google Scholar

3. Oraizi, H. and N. Noori, "Least square solution of the 3-D vector parabolic equation," J. of Electromagn. Waves and Appl., Vol. 20, No. 9, 1175-1187, 2006.
doi:10.1163/156939306777442935 Google Scholar

4. Catedra, M. F., R. P. Torres, J. Basterrecha, and E. Gago, The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics, Artech House, 1995.

5. Xu, X.Q. H. Liu, and W. Z. Zhang, "The stabilized biconjugate gradient fast Fourier transform method," Proceedings of IEEE Antennas and Propagation Society International Symposium, Vol. 2, 614-617, 2002.

6. Wallen, H. and J. Sarvas, "Translation procedures for broadband MLFMA," Progress In Electromagnetics Research, Vol. 55, 47-78, 2005.
doi:10.2528/PIER05021001 Google Scholar

7. Li, M.-K. and C. Chew, "Applying divergence-free condition in solving the volume integral equation," Progress In Electromagnetics Research, Vol. 57, 311-333, 2006.
doi:10.2528/PIER05061303 Google Scholar

8. Xie, G. Q., J. Li, L. Xie, and F. Xie, "A GL Metro Carlo EM inversion," J. of Electromagn. Waves and Appl., Vol. 20, No. 14, 1991-2000, 2006.
doi:10.1163/156939306779322756 Google Scholar

9. Al Sharkawy, M. H., V. Demir, and A. Z. Elsherbeni, "The iterative multi-region algorithm using a hybrid finite difference frequency domain and method of moment techniques," Progress In Electromagnetics Research, Vol. 57, 19-32, 2006.
doi:10.2528/PIER05071001 Google Scholar

10. Habashy, T. M., R. W. Groom, and B. Spies, "Beyond the Born and Rytov approximations: A non-linear approach to electromagnetic scattering," J. Geophys. Res., Vol. 98, No. B2, 1759-1775, 1993.
doi:10.1029/92JB02324 Google Scholar

11. Zhdanov, M. S., V. I. Dmitriev, S. Fang, and G. Hursan, "Quasi-analytical approximation and series in 3D electromagnetic modeling," Geophysics, Vol. 65, 1746-1757, 2000.
doi:10.1190/1.1444859 Google Scholar

12. Zhdanov, M. S. and S. Fang, "Quasilinear approximation in 3- D electromagnetic modeling," Geophys., Vol. 61, No. 3, 646-665, 1996.
doi:10.1190/1.1443994 Google Scholar

13. Song, L.-P. and Q. H. Liu, "A new approximation to threedimensional electromagnetic scattering," IEEE Geosci. Remote Sens. Letters, Vol. 2, No. 2, 238-242, 2005.
doi:10.1109/LGRS.2005.846836 Google Scholar

14. Singer, B. S. and E. B. Fainberg, "Generalization of the iterative-dissipative method for modeling electromagnetic fields in nonuniform media with displacement currents," J. Appl. Geophys., Vol. 34, 41-46, 1995.
doi:10.1016/0926-9851(95)00002-J Google Scholar

15. Pankratov, O. V., D. B. Avdeev, and A. V. Kuvshinov, "Electromagnetic field scattering in a heterogeneous earth: A solution to the forward problem," Physics of the Solid Earth, Vol. 31, 201-209, 1995. Google Scholar

16. Zhdanov, M. S. and S. Fang, "Quasi-linear series in threedimensional electromagnetic modeling," Radio Science, Vol. 32, No. 6, 2168-2188, 1997.
doi:10.1029/97RS02284 Google Scholar

17. Gao, G. and C. Torres-Verdin, "High-order generalized extended Born approximation for electromagnetic scattering," IEEE Trans. Antennas Propag., Vol. 54, No. 4, 1243-1256, 2006.
doi:10.1109/TAP.2006.872671 Google Scholar

18. Eidesmo, T., S. Ellingsrud, L. M. MacGregor, S. Constable, M. C. Sinha, S. Johansen, F. N. Kong, and H. Westerdahl, "Sea Bed Logging (SBL), a new method for remote and direct identification of hydrocarbon filled layers in deepwater areas," First Break, Vol. 20, No. 3, 144-152, 2002. Google Scholar

19. Hohmann, G. W., "Three-dimensional induced polarization and electromagnetic modeling," Geophys., Vol. 40, No. 2, 309-324, 1975.
doi:10.1190/1.1440527 Google Scholar

20. Wannamaker, P. E., G. W. Hohmann, and W. A. SanFilipo, "Electromagnetic modelling of three-dimensional bodies in layered earths using integral equations," Geophysics, Vol. 49, No. 1, 60-74, 1983.
doi:10.1190/1.1441562 Google Scholar

21. Eroglu, A. and J. K. Lee, "Dyadic Green's functions for an electrically gyrotropic medium," Progress In Electromagnetics Research, Vol. 58, 223-241, 2006.
doi:10.2528/PIER05070203 Google Scholar

22. Born, M., Optics, Springer-Verlag, 1933.

23. Gao, G., C. Torres-Verdin, and S. Fang, "Fast 3D modeling of borehole induction measurements in dipping and anisotropic formations using a novel approximation technique," Petrophysics, Vol. 45, 335-349, 2004. Google Scholar

24. Avdeev, D. B. and A. D. Avdeeva, "A rigorous three-dimensional magnetotelluric inversion," Progress In Electromagnetics Research, Vol. 62, 41-48, 2006.
doi:10.2528/PIER06041205 Google Scholar

25. Gao, G., C. Torres-Verdin, and T. M. Habashy, "Analytical techniques to evaluate the intergrals of 2D and 3D spatial dyadic Green's functions," Progress In Electromagnetics Research, Vol. 52, 47-80, 2005.
doi:10.2528/PIER04070201 Google Scholar

Dr. Leiv-J. Gelius